$\dfrac{ -7i + 2j }{ -2 } = \dfrac{ 2i - 6k }{ -8 }$ Solve for $i$.
Multiply both sides by the left denominator. $\dfrac{ -7i + 2j }{ -{2} } = \dfrac{ 2i - 6k }{ -8 }$ $-{2} \cdot \dfrac{ -7i + 2j }{ -{2} } = -{2} \cdot \dfrac{ 2i - 6k }{ -8 }$ $-7i + 2j = -{2} \cdot \dfrac { 2i - 6k }{ -8 }$ Multiply both sides by the right denominator. $-7i + 2j = -2 \cdot \dfrac{ 2i - 6k }{ -{8} }$ $-{8} \cdot \left( -7i + 2j \right) = -{8} \cdot -2 \cdot \dfrac{ 2i - 6k }{ -{8} }$ $-{8} \cdot \left( -7i + 2j \right) = -2 \cdot \left( 2i - 6k \right)$ Distribute both sides $-{8} \cdot \left( -7i + 2j \right) = -{2} \cdot \left( 2i - 6k \right)$ ${56}i - {16}j = -{4}i + {12}k$ Combine $i$ terms on the left. ${56i} - 16j = -{4i} + 12k$ ${60i} - 16j = 12k$ Move the $j$ term to the right. $60i - {16j} = 12k$ $60i = 12k + {16j}$ Isolate $i$ by dividing both sides by its coefficient. ${60}i = 12k + 16j$ $i = \dfrac{ 12k + 16j }{ {60} }$ All of these terms are divisible by $4$ $i = \dfrac{ {3}k + {4}j }{ {15} }$